In [1]}, the consequence of the local (i.e. space-dependent) Carrollian boost invariance of the action of a classical theory in a general curved Carrollian background of arbitrary dimensions was investigated. It was shown that the EM tensor off-shell satisfies such a condition that, for flat Carrollian background, simplifies into \(T^i_{\hspace{4.2679pt}t}=0\) . Our conclusion agrees with that since the \(1+1\) D TSCT is already a local flat-Carrollian boost.
